Full diffeomorphism and Lorentz invariance in 4D ${\cal N}=1$ superfield description of 6D SUGRA

TL;DR

This paper completes the 4D ${ m abla}=1$ superfield formulation of 6D supergravity by including superfields for the sechsbein and second gravitino, ensuring invariance under extra-dimensional diffeomorphisms and Lorentz transformations.

Contribution

It introduces superfields for the sechsbein and second gravitino, enabling full invariance under 6D diffeomorphisms and Lorentz transformations in 4D superfield supergravity.

Findings

Superfield transformation laws for extra-dimensional fields derived.

Action invariance under extended superdiffeomorphisms demonstrated.

Reduces correctly to known 5D supergravity description.

Abstract

We complete the four-dimensional ${\cal N}=1$ superfield description of six-dimensional supergravity. The missing ingredients in the previous works are the superfields that contain the sechsbein $e_4^{\;\;\underline{\nu}}$, $e_5^{\;\;\underline{\nu}}$, $e_\mu^{\;\;\underline{4}}$, $e_\mu^{\;\;\underline{5}}$ and the second gravitino. They are necessary to make the action invariant under the diffeomorphisms and the Lorentz transformations involving the extra dimensions. We find the corresponding superfield transformation laws, and show the invariance of the action under them. We also check that the resultant action reproduces the known superfield description of five-dimensional supergravity through the dimensional reduction.